I have read several books that identify archaeological evidence in support of hundreds and hundreds of biblical places, cultures, and historical events. What is the archaeological evidence for the events in the Book of Mormon?

By way of clarification, archaeology has a lot to do with the study of ancient ruins. There's a passing remark in the Book of Mormon indicating that the civilizations in question did a lot of their construction with wood, which unfortunately does not tend to leave much in the way of ruins. Are you only looking for archaeological evidence? If not, would you mind restating your question to describe what you are looking for?
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Mason Wheeler♦Nov 1 '11 at 16:26

The introductory to the BOM implores you to pray to God about the authenticity of the book. That's about as close as you'll get to proving it one way or the other. For every bit of evidence supporting it, you will find an equal amount refuting that evidence.
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BubblesFeb 6 at 0:09

2 Answers
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Depending on the scope of this question, it can be very difficult to give any satisfactory answer to. Archaeology primarily concerns itself with artifacts that have been left behind from ancient days, whereas the Book of Mormon deliberately avoids going into too much detail on the culture of its people and explaining details that might aid archaeological research, preferring to focus on more sacred matters. Also, it appears that their preferred method of construction was in wood, which doesn't lend itself well to the generation of archaeological ruins:

3 And it came to pass in the forty and sixth [year], ... there were an exceedingly great many who departed out of the land of Zarahemla, and went forth unto the land northward to inherit the land.

...

7 And there being but little timber upon the face of the land, nevertheless the people who went forth became exceedingly expert in the working of cement; therefore they did build houses of cement, in the which they did dwell.

...

9 And the people who were in the land northward did dwell in tents, and in houses of cement, and they did suffer whatsoever tree should spring up upon the face of the land that it should grow up, that in time they might have timber to build their houses, yea, their cities, and their temples, and their synagogues, and their sanctuaries, and all manner of their buildings.

10 And it came to pass as timber was exceedingly scarce in the land northward, they did send forth much by the way of shipping.

11 And thus they did enable the people in the land northward that they might build many cities, both of wood and of cement.

So we see that they considered timber to be the preferred method of construction. When it was unavailable, they developed new techniques for constructing houses and buildings of cement, and eventually became "exceedingly expert in the working of cement," but still placed a high value on wood as a construction material. (Having lived in South America, where many modern homes are built of cement and bricks, I can certainly understand this attitude. Cement is a rather good conductor of heat, which is an undesirable quality at low latitudes!)

The cement settlements are interesting. This was once derided as a hopeless anachronism in the Book of Mormon: the working of cement was an Old World art that never existed in pre-Colombian America! Right up until the mid-twentieth century, that is, when archaeologists started finding cement settlements in the vicinity of modern-day Mexico City, built with an extremely high degree of skill ("exceedingly expert") dating back to approximately the same time as the Book of Mormon states that these colonists moved in. (As reported in Concrete Evidence for the Book of Mormon.)

However, this settlement is an exception rather than a general rule. The people in question preferred construction in wood or simply living in tents, neither of which generates much in the way of ruins. Also, Book of Mormon archaeology is at a second disadvantage when compared to Biblical archaeology: on the Biblical side, we know exactly where to start looking! Modern-day Jerusalem is located on the side of the same mountain it's been on since at least the days of Melchizedek, to give just one example.

It will not be surprising, if you understand this, to hear that much of the truly interesting archaeological and historical evidence to arise in support of the Book of Mormon actually comes from discoveries in the Old World. To continue the earlier theme of Book of Mormon details once thought to be ridiculous, the book mentions two different men by the name of Alma. This was once held up as proof of Joseph Smith's hopeless inexperience: Alma is a Latin name, not a Jewish name, and a feminine Latin name at that!

...until the Dead Sea Scrolls were discovered, more than a century after the publication of the Book of Mormon, that is. One of the scrolls contains a reference to one "Alma, son of Judah." Oops.

Then we have the Lachish Letters, a group of clay tablets found in the ruins of an ancient Jewish city, dating back to just a few years after the start of the Book of Mormon. They describe several non-Biblical details of the local political climate which fit hand-in-hand with the corresponding Book of Mormon narrative. LDS scholar Hugh Nibley wrote a very detailed article on the letters, summarizing it at the end with 18 points of remarkable similarity between the two, and concluding that

Other parallels may be added to taste, but this should be enough to show that Joseph Smith was either extravagantly lucky in the opening episodes of his Book of Mormon—that should be demonstrated by computer—or else he had help from someone who knew a great deal.

Entire volumes have been written, and then, sadly, largely ignored, regarding the authenticity of the introductory chapters of the Book of Mormon, the ones that deal with travels in the Old World. To give just one example which is freely available online, see Lehi in the Desert, again by Dr. Nibley. He examines cultural details, religious and dream imagery, historical background, and even the names used, and shows that it is all remarkably consistent with the time and place it purports to originate from.

Stronger than any external evidence for or against the authenticity of the Book of Mormon, though, is internal evidence. There is a word for a literary work that claims a certain authorship but does not actually originate the way it claims to: forgery. And there are well-established tools and techniques for the detection of literary forgery, and they do not require the support of external evidence. But strangely enough, these formal methods don't tend to get applied in adversarial analyses of the Book of Mormon.

On the surface of it, there's no good reason not to; the Book of Mormon is a forger's nightmare! A fairly large work, claiming to be historical in nature, disseminated as widely as possible and inviting all to read and critically examine it? What is the forger thinking?!? This violates every rule of producing a successful forgery! But the two most important principles in the detection of literary forger tend to be consistently ignored:

Begin with the assumption that the work is genuine, and

no external evidence is required to expose a forgery of any significant size; internal inconsistencies alone will do that every time.

I could go on, (and on and on and on; as I said before, there have been entire volumes written on the subject,) but this answer is getting to be too long as it is. Suffice it to say that a large corpus of evidence exists which, while not enough to conclusively prove the truthfulness of the Book of Mormon, (they haven't even managed to do that with the Bible, so it would be unfair to hold another work that claims to be scripture to such a high standard,) definitely demonstrates that the book is worthy of serious attention and consideration.

The claims in the answer that textual analysis is overwhelming supportive are refuted with a short internet search. There is a very specific critique based on old world animals in the Americas 800 years too soon. 1 Nephi 18:25 The people arrive in the promised land. About 591–589 B.C. "And it came to pass that we did find upon the land of promise, . . . , that there were beasts in the forests . . . , both the cow and the ox, and the ass and the horse, and the goat and the wild goat, and all manner of wild animals, . . . . " ALL these animals arrived after Columbus.
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George WhiteFeb 24 '14 at 5:26

@GeorgeWhite: Those claims have been around for a long time, and there isn't enough space in a SE comment to answer them all, but suffice it to say this critique is nowhere near as simple as it appears on the surface. When Europeans arrived, they called native animals such as llamas "goats," for example, so it's reasonable to think other Old World emigrants would as well. And pre-Colombian horse bones have been found in various places in the New World. The evidence is not conclusive, but it's more than enough to show that the evidence against is not conclusive either.
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Mason Wheeler♦Feb 24 '14 at 6:11

Thanks - I believe things are usually more complicated that they might seem at first. However, in your answer you seem to imply that the internal textual evidence is all but overwhelming positive. Not mentioning in the long answer that large potential holes are right on the surface hurts the answer in my opinion. Every animal mention is widely thought to be an old world animal? Are there any mentions of odd new world animals that would have been strange to these early settlers?
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George WhiteFeb 24 '14 at 6:36

@GeorgeWhite: The thing about external evidence is, it's external. It depends on the state of the outside world for its validity, and that can change. In the case of the Book of Mormon, it has, several times, showing again and again a solid basis for things once thought to be ridiculously anachronistic. But the internal evidence is self-contained. The book says what it says, and new discoveries aren't going to change the text.
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Mason Wheeler♦Feb 24 '14 at 13:40

There is a large and growing body of work by LDS scholars offering archaeological and anthropological evidence in support of the Book of Mormon: an introduction to it may be found on the FairMormon Wiki, However, it is not expected that such evidence will ever be conclusive.